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Finding the next terms of an arithmetic sequence with whole numbers




A sequence is a set or series of numbers that follow a certain rule.

For example –

1, 3, 5, 7… is a sequence of numbers that follow a rule: To find a number in this sequence we add 2 to the previous number.

An Arithmetic sequence is a series of numbers where each number is found by adding or subtracting a constant from the previous number.

The constant in an arithmetic sequence is known as the common difference ‘d`.

In general, we write an arithmetic sequence as follows…

a, a + d, a + 2d , a + 3d, a + 4d…

where, a is the first term and d is the common difference.

The rule for finding nth term of an arithmetic sequence

an = a + (n-1)d

an is the nth term, d is the common difference.

The first three terms of an arithmetic sequence are 13, 18, and 23. Find the next two terms of this sequence.

Solution


Step 1:

Given the arithmetic sequence 13, 18 and 23. The common difference is

18 -13 = 23 -18 = 5 or d = 5

Step 2:

The next two terms in the sequence are 23 + 5 and 28 + 5 or 28 and 33

So the answer is 28 and 33

The first three terms of an arithmetic sequence are 11, 4, and -3. Find the next two terms of this sequence.

Solution


Step 1:

Given the arithmetic sequence 11, 4 and -3. The common difference is

4 -11 = -3 – 4 = -7 or d = -7

Step 2:

The next two terms in the sequence are -3 -7 and -10 -7 or -10 and -17

So the answer is -10 and -17